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Burton was born in Edinburgh to John Hill Burton, a lawyer and amateur historian, who had written two books on economics, which had received attention in Japan. His mother was Katherine, daughter of Dr Cosmo Innes, one of Scotland's foremost amateur photographers. He was also a childhood friend of Sir Arthur Conan Doyle, who turned to him for background information for The Engineer's Thumb; Doyle's book, The Firm of Girdlestone, is dedicated to Burton.[1]

Burton studied at Edinburgh Collegiate School, but instead of going on to university, from 1873 he signed up for a five-year apprenticeship with the innovative hydraulic and mechanical engineers Brown Brothers & Co. Ltd at the Rosebank Ironworks in Edinburgh. Rising to become chief draftsman, he left the firm in 1879 to enter partnership with his uncle Cosmo Innes in London designing water systems. In 1881 he became Resident Engineer to the London Sanitary Protection Association.[2]

In May 1887 he was invited by the Meiji government to assume the post of first unofficial professor of sanitary engineering at Tokyo Imperial University (he lectured as an engineer), at a time when the country was dealing with several serious epidemics, notably cholera. His appointment was unusual in that Burton was largely self-educated, and did not come with the impressive educational or professional credentials that many of his contemporaries had. It is not known who recommended Burton to the Japanese government, or what inspired him to leave a promising career in London for what he believed to be a temporary assignment in Japan.[2] He met Nagai Kyuichiro, an officer of the Sanitary Department of the Japan Home Ministry and of the Tokyo Imperial University, while Nagai was staying in London. Nagai invited him to Japan.[3]

Burton helped train a number of prominent water system engineers for nine years, and became the sole consultant engineer for the Sanitary Department of the Home Ministry, planning and managing the water and drainage systems of numerous cities, including Tokyo. His achievements are considered the starting point of Japan's environmental and sanitary engineering. The sand filtration system he built in Shimonoseki city, Yamaguchi prefecture is still functional today and produces water so pure it is bottled with Burton's picture on the label.[4]

Burton also designed Japan's first skyscraper, Ryōunkaku in Asakusa, Tokyo. This 12-story, 225-foot (68.58-metre) tall structure was the tallest building in Tokyo at the time it opened in 1890. This octagonal building gained iconic status as a symbol of modern Japan, and boasted Japan's first electric lift. It was damaged beyond repair in the 1923 Great Kanto earthquake.[2]

Burton was a noted photographer and made a substantial contribution to Japan's photographic history. He published several technical works on photography, and made a contribution in the introduction of Japanese culture to the West by sending his own photographs to various London magazines. He also did much to publicise the works of fledgling Japanese photographers in Britain.[5] Burton worked with seismologist John Milne in co writing and co photographing a book that recorded the disastrous great Earthquake of 1891. The book illustrated the plight of the Japanese people and the impact of an earthquake on their environment, in dramatic images that were printed by Ogawa Kazumasa[6][7]

In 1896, after his term at Tokyo Imperial University expired, Burton went to Japanese Formosa as an engineer, where he made outstanding contributions to improving the sanitation systems in Taiwanese cities under the authority of the Japanese Governor-General of Taiwan.[9] He then returned to Japan proper in 1899.

Burton began cohabition with a Japanese woman, Orakawa Matsu, with whom he had a daughter (Tamako) from 1892. On 19 May 1894, he married the mother of his child at a ceremony at the British Consulate in Tokyo.[2]

Burton had intended to return with his family to Scotland to meet his mother, but suddenly fell ill from a liver infection and died on 5 August 1899 at the age of 43. His grave at Aoyama Cemetery in Tokyo is marked by an impressive monument erected by his friends and former pupils.[1] In 2006, a memorial was also erected in his home town of Edinburgh, in honour of the 150th anniversary of his birth. The memorial was dedicated at the Burton family home, Craig House, now part of the Craighouse Campus of Edinburgh Napier University[10]